The unnamed player was tested on Saturday and will self-isolate for 14 days while he recovers from the virus.
The rest of Brighton’s squad will continue to train at home and in solo sessions at the team’s training ground.
Two other Brighton players, who were not named, contracted the virus several weeks ago and have reportedly recovered.
“Unfortunately we have had a third player test positive just yesterday,” Barber told Sky Sports News.
“Despite all the measures we have all been taking over the last few weeks, when the players haven’t been involved in taking any significant training at all, we have still suffered another player testing positive for the virus.
“There are concerns and I think it is normal for all clubs to have those concerns.
“We want to make sure we do all that we can so the protocols that are put into place are safe and secure and mitigate the risk.”
In Germany, Bundesliga 2 side Dynamo Dresden have put their entire squad and coaching staff into two-week
isolation after two players tested positive for coronavirus.
The Bundesliga and Bundesliga 2 are due to restart on May 16.
Brighton’s latest positive test comes ahead of Monday’s Premier League meeting, where clubs are expected to debate the plan to complete the season behind closed doors at neutral venues and vote on whether player contracts will be extended until the end of the rescheduled campaign.
The Premier League would like to restart the season in June and play the remaining 92 fixtures by August.
Barber has been critical of the neutral venue idea, insisting that the campaign should still be played on a home-and-away basis as Brighton battle to avoid relegation.
Norwich, Watford and Aston Villa were in the relegation zone when the Premier League was suspended because of the health crisis on March 13.
– ‘Self-interest’ –
Brighton have received criticism for their vocal stance, but Barber insists all clubs will act with a degree of self-interest.
“People will accuse us of self-interest, I totally understand that, but at this stage of the season there is self-interest at every level of the table,” he added.
“There is as much self-interest at the top as there is at the bottom, there is as much self-interest in the middle as there is at the bottom.
“Everyone has different objectives for the season and we are all looking to play out the season, if it is safe to do so.
We really do want to play and we want to make sure the competition stays as fair as it can be despite these exceptional circumstances that we are facing.”
Aston Villa and Watford have joined Brighton in speaking out against the neutral stadium plan.
But Crystal Palace chairman Steve Parish has backed the 20 clubs to eventually come to a consensus.
“There are no easy answers, we have to work through it as a collective and I think we will and come out with a consensus in the end,” he told the BBC.
“(The meeting) is another part of the journey in trying to get football back. We would be derelict in our duty if we did not find a way for the game to come back.
“It may prove beyond us, we have huge challenges in order to get it back to complete the season but we are planning on doing so.”